It may the technologically or medically beneficial to know understand microstructure of an object or tissue. For instance knowing the number of particles or blood vessels within a particular volume or cross section may impart information descriptive of the structure or even be useful in assisting in diagnosis of a pathology.
In PCT patent application WO 00/70362 Magnetic Resonance Elastography is used to measure Young's modulus at a single frequency using longitudinal waves.
In Sinkus et. al. “Viscoelastic shear properties of in vivo breast lesions measured by MR elastography,” Magnetic Resonance Imaging 23 (2005) 159-165 a technique for measuring the shear viscosity and shear modulus using magnetic resonance imaging.
Magnetic Resonance Elastography is reviewed in the journal article Mariappan et. al., “Magnetic Resonance Elastography: A Review,” Clin. Anat. 2010 July; 23(5) 497-511; doi:10.1002/ca.21006.